In this paper, we proposed an Lagrangian based heuristic algorithm for optimal production plan for the LED manufacturing system which is composed of wafer FAB and package assembly lines. To develop an algorithm that can minimize production-related costs and generate optimal production plans in an appropriate time, we modeled the given problem mathematically in MIP, and applied the Lagrangian relaxation method. We performed computational test with randomly generated problems based on the real data of the considering manufacturing facility, and the proposed heuristics in this study can give near optimal production plan within reasonable time.